Scholarly article on topic 'Predictions of the constrained exceptional supersymmetric standard model'

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Abstract of research paper on Physical sciences, author of scientific article — P. Athron, S.F. King, D.J. Miller, S. Moretti, R. Nevzorov

Abstract We discuss the predictions of a constrained version of the exceptional supersymmetric standard model (cE6SSM), based on a universal high energy soft scalar mass m 0 , soft trilinear coupling A 0 and soft gaugino mass M 1 / 2 . We predict a supersymmetry (SUSY) spectrum containing a light gluino, a light wino-like neutralino and chargino pair and a light bino-like neutralino, with other sparticle masses except the lighter stop being much heavier. In addition, the cE6SSM allows the possibility of light exotic colour triplet charge 1/3 fermions and scalars, leading to early exotic physics signals at the LHC. We focus on the possibility of a Z ′ gauge boson with mass close to 1 TeV, and low values of ( m 0 , M 1 / 2 ) , which would correspond to an LHC discovery using “first data”, and propose a set of benchmark points to illustrate this.

Academic research paper on topic "Predictions of the constrained exceptional supersymmetric standard model"

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Physics Letters B

www.elsevier.com/locate/physletb

Predictions of the constrained exceptional supersymmetric standard model

P. Athrona, S.F. Kingb, D.J. Millerc'*, S. Morettib, R. Nevzorov

a ¡nstitut fur Kern- und Teilchenphysik, TU Dresden, D-01062, Germany b School of Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ, UK c Department of Physics and Astronomy, University of Glasgow, Glasgow, G12 8QQ, UK

ARTICLE INFO

Article history:

Received 3 February 2009

Received in revised form 23 September

Accepted 19 October 2009 Available online 21 October 2009 Editor: G.F. Giudice

ABSTRACT

We discuss the predictions of a constrained version of the exceptional supersymmetric standard model (cE6SSM), based on a universal high energy soft scalar mass m0, soft trilinear coupling A0 and soft gaugino mass Mi/2. We predict a supersymmetry (SUSY) spectrum containing a light gluino, a light wino-like neutralino and chargino pair and a light bino-like neutralino, with other sparticle masses except the lighter stop being much heavier. In addition, the cE6SSM allows the possibility of light exotic colour triplet charge 1 /3 fermions and scalars, leading to early exotic physics signals at the LHC. We focus on the possibility of a Z' gauge boson with mass close to 1 TeV, and low values of (m0, M1/2), which would correspond to an LHC discovery using "first data", and propose a set of benchmark points to illustrate this.

© 2009 Elsevier B.V. All rights reserved.

1. Introduction

The minimal supersymmetric standard model (MSSM) [1] provides a very attractive supersymmetric extension of the standard model (SM). Its superpotential contains the bilinear term iHdHu, where Hd,u are the two Higgs doublets which develop vacuum expectation values (VEVs) at the weak scale and i is the supersym-metric Higgs mass parameter which can be present before SUSY is broken. However, despite its attractiveness, the MSSM suffers from the i problem: one would naturally expect i to be either zero or of the order of the Planck scale, while, in order to get the correct pattern of electroweak symmetry breaking (EWSB), i is required to be in the TeV range.

It is well known that the i term of the MSSM can be generated effectively by the low energy VEV of a singlet field S via the interaction XSHdHu. However, although an extra singlet super-field seems like a minor modification to the MSSM, which does no harm to either gauge coupling unification or neutralino dark matter, its introduction leads to an additional accidental global U (1) (Peccei-Quinn (PQ) [2]) symmetry which will result in a weak scale massless axion when it is spontaneously broken by (S) [3]. Since such an axion has not been observed experimentally, it must

* Corresponding author.

E-mail addresses: p.athron@physics.gla.ac.uk (P. Athron), sfk@hep.phys.soton.ac.uk (S.F. King), d.miller@physics.gla.ac.uk (D.J. Miller), stefano@phys.soton.ac.uk (S. Moretti), nevzorov@phys.soton.ac.uk (R. Nevzorov).

1 On leave of absence from the Theory Department, ITEP, Moscow, Russia.

be removed somehow. This can be done in several ways resulting in different non-minimal SUSY models, each involving additional fields and/or parameters [4,5]. For example, the classic solution to this problem is to introduce a singlet term S3, as in the next-to-minimal supersymmetric standard model (NMSSM) [4], which reduces the PQ symmetry to the discrete symmetry Z3. However the subsequent breaking of a discrete symmetry at the weak scale can lead to cosmological domain walls which would overclose the Universe.

A cosmologically safe solution to the axion problem of singlet models, which we follow in this Letter, is to promote the PQ symmetry to an Abelian U(1)' gauge symmetry [6]. The idea is that the extra gauge boson will eat the troublesome axion via the Higgs mechanism resulting in a massive Z' at the TeV scale. The necessary U(1)' gauge group could be a relic of the breaking of some unified gauge group at high energies. Recall that the unification of gauge couplings in SUSY models allows one to embed the gauge group of the SM into Grand Unified Theories (GUTs) based on simple gauge groups such as SU(5), S0(10) or E6. In particular the E6 symmetry can be broken to the rank-5 subgroup SU(3)c x SU(2)l x U(1)y x U(1)' where in general U(1)'= U(1)x cos6 + U(\)f sin6 [7], and the two anomaly-free U(1)^ and U(1)x symmetries originate from the breakings E6 ^ S0(10) x U(1)f, S0(10) ^ SU(5) x U(1)x (for recent review see [8]).

Within the class of E6 models there is a unique choice of Abelian gauge group that allows zero charges for right-handed neutrinos and thus large Majorana masses and a high scale see-

0370-2693/$ - see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.physletb.2009.10.051

saw mechanism. This is the U (1)N gauge symmetry given by 0 = arctan and defines the so-called exceptional supersym-metric standard model (E6SSM) [9]. The extra U(1)N gauge symmetry survives to low energies and forbids a bilinear term ¡iHfHu in the superpotential but allows the

interaction XSHdHy. At the electroweak (EW) scale. the scalar component of the SM singlet superfield S acquires a non-zero VEV, (S} =s/V2, breaking U (1)N and yielding an effective i = Xs/\[2 term. Thus the ¡i problem in the E6SSM is solved in a similar way to the NMSSM, but without the accompanying problems of singlet tadpoles or domain walls. In this model low energy anomalies are cancelled by complete 27 representations of E6 which survive to low energies, with E6 broken at the high energy GUT scale.

In this Letter we discuss some of the predictions of particular relevance to the LHC from a constrained version of the E6SSM (cE6SSM), based on a universal high energy soft scalar mass m0, soft trilinear coupling A0 and soft gaugino mass Mi/2. Our primary focus is on the most urgent regions of parameter space which involve low values of (m0, M^/2) and low Z' gauge boson masses which would correspond to an early LHC discovery using "first data". To illustrate these features we propose and discuss a set of "early discovery" benchmark points, each associated with a Z' gauge boson mass around 1 TeV and (m0, M\/2) below 1 TeV, which would lead to an early indication of the cE6SSM at the LHC. We find a SUSY spectrum consisting of a light gluino of mass ~M3, a light wino-like neutralino and chargino pair of mass ~M2, and a light bino-like neutralino of mass ~M1, where Mi are the low energy gaugino masses, which are typically driven small by renormalisation group (RG) running. Sfermions are generally heavier, but there can be an observable top squark. There may also be light exotic colour triplet charge 1/3 fermions and scalars, whose masses are controlled by independent Yukawa couplings. Some first results have already been trailed at conferences [10] and a longer paper containing full details of the analysis is about to appear [11].

In Section 2 we briefly review the E6SSM, then in Section 3 we introduce the cE6SSM. Section 4 describes the experimental and theoretical constraints and Section 5 discusses the aforementioned predictions of the cE6SSM elucidated by five "early discovery" benchmark points. Section 6 concludes the Letter.

2. The E6SSM

One of the most important issues in models with additional Abelian gauge symmetries is the cancellation of anomalies. In E6 theories, if the surviving Abelian gauge group factor is a subgroup of E6, and the low energy spectrum constitutes a complete 27 representation of E6, then the anomalies are cancelled automatically. The 27i of E6, each containing a quark and lepton family, decompose under the SU(5) x U(1)N subgroup of E6 as follows:

Table 1

The U(1) y and U (1)N charges of matter fields in the EgSSM, where QtN and Qy are here defined with the correct E6 normalisation factor required for the RG analysis.

27i ^ (10,1)i + (5*, 2i + (5*, —3)i + (5, —2)i + (1, 5)i + (1, 0)i.

The first and second quantities in the brackets are the SU(5) representation and extra U(1)N charge while i is a family index that runs from 1 to 3. From Eq. (1) we see that, in order to cancel anomalies, the low energy (TeV scale) spectrum must contain three extra copies of 5* + 5 of SU(5) in addition to the three quark and lepton families in 5* + 10. To be precise, the ordinary SM families which contain the doublets of left-handed quarks Q i and leptons Li, right-handed up- and down-quarks (uC and dci) as well as right-handed charged leptons, are assigned to (10,1)i + (5*, 2)i. Right-handed neutrinos Nic should be associated with the last term in Eq. (1), (1, 0)i. The next-to-last term in Eq. (1), (1, 5)i, represents SM-type singlet fields Si which carry non-zero U(1)N charges and

Q uc dc L ec Nc S H2 H1 D D H' H'

/1QY 1 6 2 3 1 1 3 2 1 0 0 1 2 1 1 2 3 1 1 3 2 1 2

V40q" 1 1 2 2 1 0 5 -2 -3 -2 —3 2 -2

therefore survive down to the EW scale. The three pairs of SU(2)-doublets (Hf and Hu) that are contained in (5*, —3)i and (5, —2)i have the quantum numbers of Higgs doublets, and we shall identify one of these pairs with the usual MSSM Higgs doublets, with the other two pairs being "inert" Higgs doublets which do not get VEVs. The other components of these SU(5) multiplets form colour triplets of exotic quarks Di and Di with electric charges —1/3 and +1 /3 respectively. The matter content and correctly normalised Abelian charge assignment are in Table 1.

We also require a further pair of superfields H' and H' with a mass term ¡lH'H' from incomplete extra 27' and 27' representations to survive to low energies to ensure gauge coupling unification. Because H' and H' originate from 27' and 27' these supermultiplets do not spoil anomaly cancellation in the considered model. Our analysis reveals that the unification of the gauge couplings in the E6SSM can be achieved for any phenomenolog-ically acceptable value of a3(MZ), consistent with the measured low energy central value [12].2

Since right-handed neutrinos have zero charges they can acquire very heavy Majorana masses. The heavy Majorana right-handed neutrinos may decay into final states with lepton number L = ±1, thereby creating a lepton asymmetry in the early Universe. Because the Yukawa couplings of exotic particles are not constrained by the neutrino oscillation data, substantial values of CP-violating lepton asymmetries can be induced even for a relatively small mass of the lightest right-handed neutrino (M1 ~ 106 GeV) so that successful thermal leptogenesis may be achieved without encountering any gravitino problem [14].

The superpotential of the E6SSM involves a lot of new Yukawa couplings in comparison to the SM. In general these new interactions violate baryon number conservation and induce nondiagonal flavour transitions. To suppress baryon number violating and flavour changing processes one can postulate a Z2H symmetry under which all superfields except one pair of Hif and Hiu (say Hf = H3 and Hu = Hy) and one SM-type singlet field (S = S3) are odd. The Z2H symmetry reduces the structure of the Yukawa interactions, and an assumed hierarchical structure of the Yukawa interactions allows to simplify the form of the E6SSM superpotential substantially. Keeping only Yukawa interactions whose couplings are allowed to be of order unity leaves us with

W E6SSM - XS (HdHu ) + Xa S(Hda Hua) + KiS (DiDi)

+ ht (HuQ )tc + hb (HfQ )bc + hT(HfL)T c + ¡'(H' H'),

where = 1, 2 and i = 1, 2, 3, and where the superfields L = L3, Q = Q3, tc = u3, bc = dc3 and tc = ec3 belong to the third generation and Xi, Ki are dimensionless Yukawa couplings with X = X3. Here we assume that all right-handed neutrinos are relatively heavy so that they can be integrated out.3 The SU(2)L doublets

2 The two superfields H' and H' may be removed from the spectrum, thereby avoiding the ¡l problem, leading to unification at the string scale [13]. However we shall not pursue this possibility in this Letter.

3 We shall ignore the presence of right-handed neutrinos in the subsequent RG

analysis.

Hu and Hd, which are even under the Z2H symmetry, play the role of Higgs fields generating the masses of quarks and leptons after EWSB. The singlet field S must also acquire a large VEV to induce sufficiently large masses for the Z' boson. The couplings Xi and k; should be large enough to ensure the exotic fermions are sufficiently heavy to avoiding conflict with direct particle searches at present and former accelerators. They should also be large enough so that the evolution of the soft scalar mass m2S of the singlet field S results in negative values of m2S at low energies, triggering the breakdown of the U (1)N symmetry.

However the Zi/ can only be approximate (otherwise the exotics would not be able to decay). To prevent rapid proton decay in the E6SSM a generalised definition of R-parity should be used. We give two examples of possible symmetries that can achieve that. If Hd, Hu, Si, Di, Di and the quark superfields (Qi, uc, dc) are even under a discrete Z2L symmetry while the lepton super-fields (Li,eic, Nic) are odd (Model I) then the allowed superpotential is invariant with respect to a U (1)B global symmetry. The exotic Di and Di are then identified as diquark and anti-diquark, i.e. BD = -2/3 and Bd = 2/3. An alternative possibility is to assume that the exotic quarks Di and Di as well as lepton superfields are all odd under ZB whereas the others remain even. In this case (Model II) the D and Di are leptoquarks [9].

After the breakdown of the gauge symmetry, Hu, Hd and S form three CP-even, one CP-odd and two charged states in the Higgs spectrum. The mass of one CP-even Higgs particle is always very close to the Z' boson mass MZ>. The masses of another CP-even, the CP-odd and the charged Higgs states are almost degenerate. Furthermore, like in the MSSM and NMSSM, one of the CP-even Higgs bosons is always light irrespective of the SUSY breaking scale. However, in contrast with the MSSM, the lightest Higgs boson in the E6SSM can be heavier than 110-120 GeV even at tree level. In the two-loop approximation the lightest Higgs boson mass does not exceed 150-155 GeV [9]. Thus the SM-like Higgs boson in the E6SSM can be considerably heavier than in the MSSM and NMSSM, since it contains a similar F-term contribution as the NMSSM but with a larger maximum value for X(mt ) as it is not bounded as strongly by the validity of perturbation theory up to the GUT scale [9]. However in the considered "early discovery" benchmark points in this Letter, it will always be close to the current LEP2 limit.

3. The constrained E6SSM

The simplified superpotential of the E6SSM involves seven extra couplings (i, k; and Xi) as compared with the MSSM with i = 0. The soft breakdown of SUSY gives rise to many new parameters. The number of fundamental parameters can be reduced drastically though within the constrained version of the E6SSM (cE6SSM). Constrained SUSY models imply that all soft scalar masses are set to be equal to m0 at some high energy scale MX, taken here to be equal to the GUT scale, all gaugino masses Mi (MX) are equal to M1/2 and trilinear scalar couplings are such that Ai(MX) = A0. Thus the cE6SSM is characterised by the following set of Yukawa couplings, which are allowed to be of the order of unity, and universal soft SUSY breaking terms,

Xi (Mx), ki (Mx), ht (Mx), hb(Mx), -t(Mx),

m0, M1/2, A0, (3)

where ht(MX), hb(MX) and hT(MX) are the usual t-quark, b-quark and t-lepton Yukawa couplings, and Xi(MX), Ki(MX) are the extra Yukawa couplings defined in Eq. (2). The universal soft scalar and

trilinear masses correspond to an assumed high energy soft SUSY breaking potential of the universal form,

V soft = mg27; 27? + A0 Yijk27i 27 j 27k + h.c., (4)

where Y ijk are generic Yukawa couplings from the trilinear terms in Eq. (2) and the 27i represent generic fields from Eq. (1), and in particular those which appear in Eq. (2). Since Z2H symmetry forbids many terms in the superpotential of the E6SSM it also forbids similar soft SUSY breaking terms in Eq. (4). To simplify our analysis we assume that all parameters in Eq. (3) are real and M1/2 is positive. In order to guarantee correct EWSB m02 has to be positive. The set of cE6SSM parameters in Eq. (3) should in principle be supplemented by \i! and the associated bilinear scalar coupling B'. However, since i' is not constrained by the EWSB and the term iH'H' in the superpotential is not suppressed by E6, the parameter i will be assumed to be ~10 TeV so that H' and H' decouple from the rest of the particle spectrum. As a consequence the parameters B' and i are irrelevant for our analysis.

To calculate the particle spectrum within the cE6SSM one must find sets of parameters which are consistent with both the high scale universality constraints and the low scale EWSB constraints. To evolve between these two scales we use two-loop renormalisation group equations (RGEs) for the gauge and Yukawa couplings together with two-loop RGEs for Ma(Q) and A;(Q) as well as one-loop RGEs for mf( Q). Q is the renormalisation scale. The RGE evolution is performed using a modified version of SOFTSUSY 2.0.5 [15] and the RGEs for the E6SSM are presented in a longer paper [11]. The details of the procedure we followed are summarized below.

1. The gauge and Yukawa couplings are determined independently of the soft SUSY breaking mass parameters as follows:

(i) We choose input values for s = V2(S) and tan/ = v2/v 1 (where v2 and v1 are the usual VEVs of the Higgs fields Hu and Hd) as defined by our scenario.

(ii) We set the gauge couplings g1 , g2 and g3 equal to the experimentally measured values at MZ .

(iii) We fix the low energy Yukawa couplings ht, hb, and h t using the relations between the running masses of the fermions of the third generation and VEVs of the Higgs fields, i.e.

mt (Mt) =

mT(Mt) =

ht (Mt )v

hT(Mt )v

cos /.

mb (Mt) = cos

(iv) The gauge and Yukawa couplings are then evolved up to the GUT scale MX. Using the beta functions for QED and QcD, the gauge couplings are first evolved up to mt. Since we are employing two-loop RGEs in the SUSY preserving sector, we include one estimated threshold scale for the masses of the superpartners of the SM particles, TMSSM, and one for the masses of the new exotic particles, TESSM. Since these are common mass scales we neglect mass splitting within each group of particles. So between mt and TMSSM we evolve these gauge and Yukawa couplings with SM RGEs and between TMSSM and Tessm we employ the MSSM RGEs. At Tessm the values of E6SSM gauge and Yukawa couplings, g1, g2, g3, ht, hb and hT, form a low energy boundary condition for what follows. Initial low energy estimates of the new E6SSM Yukawa couplings, Xi and Ki are also input here, and all SUSY preserving couplings are evolved up to the high scale using the two-loop E6SSM RGEs.

(v) At the GUT scale MX we set g1(MX) = g2(MX) = g3(MX) = gj (MX) = g0 and select values for k; (Mx) and X; (Mx), which

are input parameters in our procedure. An iteration is then performed between MX and the low energy scale to obtain the values of all the gauge and Yukawa couplings which are consistent with our input values for k¡(MX), Xi(MX), gauge coupling unification and our low scale boundary conditions, derived from experimental data.

2. Having completely determined the gauge and Yukawa couplings, the low energy soft SUSY breaking parameters are then determined semi-analytically as functions of the GUT scale values of Ao, M1/2 and mo. They take the form,

m2(Q) = ai(Q)Ml/2 + bi(Q)A2 + c¡(Q)AoM1/2 + di(Q)m20, (6)

Ai (Q) = ei (Q) Ao + fi (Q )MV2, (7)

Mi (Q) = Pi (Q) Ao + m (Q )Mi/2, (8)

where Q is the renormalisation scale. The coefficients are unknown but may be determined numerically at the low energy scale, as follows:

(i) Set Ao = M1/2 = o at MX with mo non-zero, and run the full set of E6SSM parameters down to the low scale to yield the coefficients proportional to mo in the expressions for the soft SUSY breaking parameters.

(ii) Repeat for Ao and M1/2.

(iii) The coefficient of the AoM1/2 term is determined using nonzero values of both Ao and M1/2 at MX, using the results in part (ii) to isolate this term.

3. Using the semi-analytic expressions for the soft masses from step 2 above, we then impose conditions for correct EWSB at low energy and determine sets of mo, M1/2 and Ao which are consistent with EWSB, as follows:

(i) Working with the tree-level potential Vo (to start with) we impose the minimisation conditions ^ = dvf = = o leading to a system of quadratic equations in mo, M1/2 and Ao. In this approximation, the equations can be reduced to two second order equations with respect to Ao and M1/2 which can have up to four solutions for each set of Yukawa couplings.

(ii) For each solution mo, M1/2 and Ao, the low energy stop soft mass parameters are determined and the one-loop Coleman-Weinberg Higgs effective potential V1 is calculated. The new minimisation conditions for V1 are then imposed, and new solutions for mo, M1/2 and Ao are obtained.

(iii) The procedure in (ii) is then iterated until we find stable solutions. Some or all of the obtained solutions can be complex. Here we restrict our consideration to the scenarios with real values of fundamental parameters which do not induce any CP-violating effects. For some values of tan /, s and Yukawa couplings the solutions with real Ao, M1/2 and mo do not exist. There is a substantial part of the parameter space where there are only two solutions with real values of fundamental parameters. However there are also some regions of the parameters where all four solutions of the non-linear algebraic equations are real.

Although correct EWSB is not guaranteed in the cE6SSM, remarkably, there are always solutions with real Ao, M1/2 and mo for sufficiently large values of k¡ , which drive m| negative. This is easy to understand since the k¡ couple the singlet to a large multiplicity of coloured fields, thereby efficiently driving its squared mass negative to trigger the breakdown of the gauge symmetry.

4. Using the obtained solutions we calculate the masses of all exotic and SUSY particles for each set of fundamental parameters in Eq. (3).

Finally at the last stage of our analysis we vary Yukawa couplings, tan / and s to establish the qualitative pattern of the particle spectrum within the cE6SSM. To avoid any conflict with present and former collider experiments as well as with recent cosmolog-ical observations we impose the set of constraints specified in the next section. These bounds restrict the allowed range of the parameter space in the cE6SSM.

4. Experimental and theoretical constraints

The experimental constraints applied in our analysis are: mh > 114 GeV, all sleptons and charginos are heavier than ioo GeV, all squarks and gluinos have masses above 3oo GeV and the Z' boson has a mass which is larger than 861 GeV [16]. We also impose the most conservative bound on the masses of exotic quarks and squarks that comes from the HERA experiments [17], by requiring them to be heavier than 3oo GeV. Finally we require that the inert Higgs and inert Higgsinos are heavier than 1oo GeV to evade limits on Higgsinos and charged Higgs bosons from LEP.

In addition to a set of bounds coming from the non-observation of new particles in experiments we impose a few theoretical constraints. We require that the lightest SUSY particle (LSP) should be a neutralino. We also restrict our consideration to values of the Yukawa couplings Xi(MX), k¡(Mx), ht(MX), hb(MX) and hT(MX) less than 3 to ensure the applicability of perturbation theory up to the GUT scale.

In our exploration of the cE6SSM parameter space we first looked at scenarios with a universal coupling between exotic coloured superfields and the third generation singlet field S, k(Mx ) = K1t2,3(MX), and fixed the inert Higgs couplings X1>2(MX) = o.1. In fixing X1>2 like this we are deliberately preselecting for relatively light inert Higgsinos. The third generation Yukawa X = X3 was allowed to vary along with k . Splitting X3 from X12 seems reasonable since X3 plays a very special role in E6SSM models in forming the effective ^,-term when S develops a VEV. Eventually we allowed non-universal k¡ (Mx). For fixed values of tan/ = 3, 1o, 3o, we scanned over s, k, X. From these input parameters, the sets of soft mass parameters, Ao, M1/2 and mo, which are consistent with the correct breakdown of electroweak symmetry, are found. We find that for fixed values of the Yukawas the soft mass parameters scale with s, while if s and tan / are fixed, varying the Yukawas, X and k , then produces a bounded region of allowed points. The value of s determines the location and extent of the bounded regions. As s is increased the lowest values of mo and M1/2, consistent with experimental searches and EWSB requirements, increase. This is shown in Fig. 1 where the allowed regions for three different values of the singlet VEV, s = 3, 4 and 5 TeV, are compared, with the allowed regions in red, green, magenta respectively and the excluded regions in white. These regions overlap since we are finding soft masses consistent with EWSB conditions that have a non-linear dependence on the VEVs and Yukawas.

5. Predictions of the cE6SSM

5.1. Overview of the spectrum and decay signatures

5.1.1. SUSY spectrum and signatures

From Fig. 1 we see that mo > M1/2 for each value of s and also that lower M1/2 is weakly correlated with lower s and thus lower Z' masses. As is discussed in detail in Ref. [11] this bound is caused, depending on the value of tan / , either by the inert Higgs

Fig. 1. Physical solutions with tan p = 10, k1,2 = 0.1, s = 3, 4, 5 TeV fixed and k = k3 and k = k1-2,3 varying, which pass experimental constraints from LEP and Tevatron data. On the left-hand side of each allowed region the chargino mass is less than 100 GeV, while underneath the inert Higgses are less than 100 GeV or becoming tachyonic. The region ruled out immediately to the right of the allowed points is due to mh < 114 GeV. The results show that m0 > M1/2 for each value of s. They also show that higher M1/2 are correlated with higher s (and thus higher Z' masses). (For interpretation of the references to colour in this figure, the reader is referred to the web version of this Letter.)

masses being driven below their experimental limit from negative D-term contributions canceling the positive contribution from m0 or the light Higgs mass going below the LEP2 limit.

Another remarkable feature of the cE6SSM is that the low energy gluino mass parameter M3 is driven to be smaller than Mi/2 by RG running. The reason for this is that the E6SSM has a much larger (super)field content than the MSSM (three 27's instead of three 16's), so much so that at one-loop order the QCD beta function (accidentally) vanishes in the E6SSM, and at two loops it loses asymptotic freedom (though the gauge couplings remain pertur-bative at high energy). This implies that the low energy gaug-ino masses are all less than M1/2 in the cE6SSM, being given by roughly M3 ~ 0.7M1/2, M2 ~ 0.25M1/2, M1 ~ 0.15M1/2. These should be compared to the corresponding low energy values in the MSSM, M3 ~ 2.7M1/2, M2 ~ 0.8M1/2, M1 ~ 0.4M1/2. Thus, in the cE6SSM, since the low energy gaugino masses Mi are driven by RG running to be small, the lightest SUSY states will generally consist of a light gluino of mass ~M3, a light wino-like neutralino and chargino pair of mass ~M2, and a light bino-like neutralino of mass ~M1, which are typically all much lighter than the Hig-gsino masses of order ¡i = Xs/42, where X cannot be too small for correct EWSB. Since m0 > M1/2 the squarks and sleptons are also much heavier than the light gauginos.

Thus, throughout all cE6SSM regions of parameter space there is the striking prediction that the lightest sparticles always include the gluino g, the two lightest neutralinos X\, X®, and a light chargino x± . Therefore pair production of X2X2, X2X±, X^X^ and gg should always be possible at the LHC irrespective of the Z' mass. Due to the hierarchical spectrum, the gluinos can be relatively narrow states with width rg a M5/mí, comparable to that of W± and Z bosons. They will decay through g ^ qq* ^ qq + Emlss, so gluino pair production will result in an appreciable enhancement of the cross section for pp ^ qqqq + ETlss + X, where X refers to any number of light quark/gluon jets.

The second lightest neutralino decays through x2 ^ X? + ll and so would produce an excess in pp ^ till + ETlss + X, which could be observed at the LHC. Since all squarks and sleptons, as well

as new exotic particles, turn out to be rather heavy compared to the low energy wino mass, the calculation of the branching ratio Br(x° ^ x0 + ll) is very similar to that in the MSSM. This branching ratio in the MSSM is known to be very sensitive to the choice of fundamental parameters of the model. For the type of the neutralino spectra presented later, in which the second lightest neutralino is approximately wino, the lightest neutralino is approximately bino, and where the other sparticles are much heavier, Br(x2 ^ X? + U) is known to vary from 1.5% to 6% [18].

5.1.2. Exotic spectrum and signatures

Other possible manifestations of the E6SSM at the LHC are related to the presence of a Z' and exotic multiplets of matter. The production of a TeV scale Z' will provide an unmistakable and spectacular LHC signal even with first data [9]. At the LHC, the Z' boson that appears in the E6 inspired models can be discovered if it has a mass below 4-4.5 TeV [19]. The determination of its couplings should be possible if MZ> < 2-2.5 TeV [20].

When the Yukawa couplings Ki of the exotic fermions Di and Di have a hierarchical structure, some of them can be relatively light so that their production cross section at the LHC can be comparable with the cross section of tt production [9]. In the E6SSM, the Di and Di fermions are SUSY particles with negative R-parity so they must be pair produced and decay into quark-squark (if di-quarks) or quark-slepton, squark-lepton (if leptoquarks), leading to final states containing missing energy from the LSP.

The lifetime and decay modes of the exotic coloured fermions are determined by the Z2H violating couplings. If Z2H is broken significantly the presence of the light exotic quarks gives rise to a remarkable signature. Assuming that Di and Di fermions couple most strongly to the third family (s)quarks and (s)leptons, the lightest exotic Di and Di fermions decay into tb, tb, tb, tb (if they are diquarks) or tT, tTt, bvT, bvr (if they are leptoquarks). This can lead to a substantial enhancement of the cross section of either pp ^ ttbb + Emiss + X (if diquarks) or pp ^ ttTT + Efiss + X or pp ^ bb + EJ?1SS + X (if leptoquarks). Notice that SM production of ttT+t- is (aW/n)2 suppressed in comparison to the leptoquark

Table 2

The cross section of DD production at the LHC as a function of the masses of exotic quarks. For simplicity we assume that three families of exotic quarks have the same masses.

ßü [GeV] 300 400 500 700 1000 1500 2000 3000

a(pp ^ üü) [pb] 76.4 17.4 5.30 0.797 0.0889 4.94 x 10-3 4.09 x 10-4 3.51 x 10-6

decays. Therefore light leptoquarks should produce a strong signal with low SM background at the LHC. In principle the detailed LHC analyses is required to establish the feasibility of extracting the excess of tibb or tit+ t — production induced by the light exotic quarks predicted by our model.

We have already remarked that the lifetime and decay modes of the exotic coloured fermions are determined by the Z2H violating couplings. If Z2H is only very slightly broken exotic quarks may be very long lived, with lifetimes up to about 1 s. This is the case, for example, in some minimal versions of the model [13]. In this case the exotic Dj and Dj fermions could hadronize before decaying, leading to spectacular signatures consisting of two low multiplicity jets, each containing a single quasi-stable heavy D-hadron, which could be stopped for example in the muon chambers, before decaying much later.

In Table 2 we estimate the total production cross section of exotic quarks at the LHC for a few different values of their masses assuming that all masses of exotic quarks are equal (i.e. ¡ Di = ¡ D ) and all sparticles as well as other new exotic particles are very heavy. The results in Table 2 suggest that the observation of the D fermions might be possible if they have masses below about 1.5-2 TeV [9].

Similar considerations apply to the case of exotic Di and Di scalars except that they are non-SUSY particles so they may be produced singly and decay into quark-quark (if diquarks) or quark-lepton (if leptoquarks) without missing energy from the LSP. It is possible to have relatively light exotic coloured scalars due to mixing effects. The RGEs for the soft breaking masses, ml and mi , d D i D i

are very similar, with ft (ml — m2 ) = g'2M'2, resulting in comparatively small splitting between these soft masses. Consequently, mixing can be large even for moderate values of the A0, leading to a large mass splitting between the two scalar partners of the exotic coloured fermions.4 Recent, as yet unpublished, results from Tevatron searches for dijet resonances [21] rule out scalar di-quarks with mass less than 630 GeV. However, scalar leptoquarks may be as light as 300 GeV since at hadron colliders they are pair produced through gluon fusion. Scalar leptoquarks decay into quark-lepton final states through small ZH violating terms, for example D ^ tt, and pair production leads to an enhancement of pp ^ tttt (without missing energy) at the LHC.

In addition, the inert Higgs bosons and Higgsinos (i.e. the first and second families of Higgs doublets predicted by the E6SSM which couple weakly to quarks and leptons and do not get VEVs) can be light or heavy depending on their free parameters. The light inert Higgs bosons decay via Z2H violating terms which are analogous to the Yukawa interactions of the Higgs superfields, Hu and Hf. One can expect that the couplings of the inert Higgs fields would have a similar hierarchical structure as the couplings of the normal Higgs multiplets, therefore we assume the Z2H

Table 3

The "early discovery" cEeSSM benchmark points.

A B C D E

tan ß 3 10 10 10 30

ЫМх ) -0.465 -0.37 -0.378 -0.395 -0.38

h.2(Mx ) 0.1 0.1 0.1 0.1 0.1

K3(Mx ) 0.3 0.2 0.42 0.43 0.17

K1,2(MX ) 0.3 0.2 0.06 0.08 0.17

s [TeV] 3.3 2.7 2.7 2.7 3.1

M1/2 [GeV] 365 363 388 358 365

m0 [GeV] 640 537 681 623 702

A0 [GeV] 798 711 645 757 1148

mü 1 (3) [GeV] 1797 628 1465 1445 393

тъ2 (3) [GeV] 1156 1439 2086 2059 1617

ßü(3) [GeV] 1466 1028 1747 1747 1055

mü 1 (1,2) [GeV] 1797 628 520 370 393

mü2 (1,2) [GeV] 1156 1439 906 916 1617

ßü(1, 2) [GeV] 1466 1028 300 391 1055

imxc | [GeV] 1278 1052 1054 1051 1203

m„36- Mz, [GeV] 1248 1020 1021 1021 1172

|mx01 [GeV] 1220 993 992 994 1143

ms (1,2) [GeV] 1097 908 1001 961 1093

mH2(1, 2) [GeV] 468 479 627 561 704

mH, (1,2) [GeV] 165 154 459 345 220

ßH (1, 2) [GeV] 249 244 233 229 298

m0l (1,2) [GeV] 893 788 911 845 929

md1 (1,2) [GeV] 910 807 929 862 945

mh (1,2) [GeV] 910 807 929 862 945

mb (1,2) [GeV] 975 850 964 903 998

me2 (1,2,3) [GeV] 874 733 849 796 900

mei (1,2,3) [GeV] 762 631 765 708 804

mg2 [GeV] 974 841 955 894 890

m-bi [GeV] 758 668 777 712 694

mf2 [GeV] 821 734 829 772 773

mh [GeV] 493 433 546 474 463

|mx01 — |mx01 ~ |mx± | [GeV] Л3 A4 Л 2 832 684 674 685 803

mh2 — m a — mH± [GeV] 615 664 963 720 593

mh! [GeV] 114 115 115 114 119

mg [GeV] 336 330 353 327 338

|mx± | — |mx01 [GeV] 107 103 109 101 103

| m'0 | [GeV]2 Л1 59 58 61 57 58

cay predominantly into 3rd generation fermion-anti-fermion pairs j0

like H0 i ^ bb. The charged inert Higgs bosons also decay into fermion-anti-fermion pairs, but in this case it is the antiparti-

cle of the fermions' EW partner, e.g. H-

tvt . The inert Higgs

breaking interactions predominantly couple the inert Higgs bosons to the third generation. So the neutral inert Higgs bosons de-

bosons may also be quite heavy, so that the only light exotic particles are the inert Higgsinos. Similar couplings govern the decays of the inert Higgsinos; the electromagnetically neutral Higgsinos predominantly decay into fermion-anti-sfermion pairs (e.g. H0 ^ tt , H0 ^ xx*). The charged Higgsinos decays similarly but in this case the sfermion is the SUSY partner of the EW partner of the fermion

(e.g. H + ^ tb , HГ ^ tvt ).

4 Note that the diagonal entries of the exotic squark mass matrices have substan-

tial negative contributions from the U (1)N D-term quartic interactions in the scalar potential. These contributions reduce the masses of exotic squarks and also con-

tribute to their mass splitting since the U (1)N charges of Di and Di are different.

5.2. Early discovery benchmarks

5.2.1. The benchmark input parameters

In Table 3 we present a set of "early discovery" benchmark points, each associated with a Z' gauge boson mass close to 1 TeV

mhl = 114 GeV (approx. two loop) Fig. 2. Spectra for the "early discovery" benchmark points A (top left), B (top right), C (middle left), D (middle right) and E (bottom centre).

which should be discovered using first LHC data. The first block of Table 3 shows the input parameters which define the benchmark points. We have selected s = 2.7-3.3 TeV corresponding to MZ! = 1020-1250 GeV, where MZ/ ^ g'1 sQS with QS = 5/V40 and g1 ^ g1. We have also restricted ourselves to (m0, M1/2) < (700, 400) GeV leading to very light gauginos, associated with the three low gaugino masses Mj, and in addition a light stop and Higgs mass. Note that for all the benchmark points the trilinear

soft mass is fixed to lie in the range A0 = 650-1150 GeV in order to achieve EWSB.

The benchmark points cover three different values of tanp = 3, 10, 30. In each case we have taken |k31 to be larger than k12 = 0.1 (fixed) at the GUT scale. In benchmark points A, B, E (corresponding to tanp = 3, 10, 30) we have taken the Kj to be universal at the GUT scale and large enough to trigger EWSB. Since the Kj's control the exotic coloured fermion masses, this implies that all the Di and

Di fermions are all very heavy in these cases. However it is not necessary for the Ki's to be universal and these Yukawa couplings may be hierarchical as for the quark and lepton couplings. To illustrate this possibility we have considered two benchmark points, C and D, both for tan /) = 10, in which k3 ^ K1t2 at the GUT scale. In these points C, D we have taken K3 to be large enough to trigger EWSB, while allowing K1t2 to be low enough to yield light D1>2 and D12 fermion masses.

5.2.2. The benchmark spectra

The full spectrum for each of the benchmark points is given in Table 3 and illustrated in Fig. 2. The benchmark points all exhibit the characteristic SUSY spectrum described above of a light gluino g, two light neutralinos x0, X2, and a light chargino x ±. The lightest neutralino x0 is essentially pure bino, while x0 and X± are the degenerate components of the wino. Since Mi/2 < 400 GeV for all the points the (two-loop corrected) gluino mass is below 350 GeV, and the wino mass just above the LEP2 limit of 00 GeV, while the bino is around 60 GeV in each case. The question of the resulting cosmological dark matter relic abundance is not considered in this Letter but one should not regard such points with a light bino as being excluded by cosmology for reasons that will be discussed later. The Higgsino states are much heavier with the degenerate Higgsinos X30,4 and X2± having masses given by i = Xs/V2 in the range 675-830 GeV for all the benchmark points. The remaining neutralinos are dominantly singlet Higgsi-nos with masses approximately given by MZ'.

The Higgs spectrum for all the benchmark points contains a very light SM-like CP-even Higgs boson h with a mass close to the LEP limit of 1 1 5 GeV, making it accessible to LHC or even Tevatron. The heavier CP-even Higgs h2, the CP-odd Higgs A0, and the charged Higgs H± are all closely degenerate with masses in the range 600-1000 GeV making them difficult to discover. The remaining mainly singlet CP-even Higgs h3 is closely degenerate with the Z'.

For benchmarks A, B, E (corresponding to tan/) = 3, 10, 30) we have taken the Ki to be universal and the exotic coloured fermions have masses in the range 1-1.5 TeV. However, due to the mixing effect mentioned previously, we find a light exotic coloured scalar with a mass of 393 GeV for point E and one at 628 GeV for B. For benchmark points C and D, with k3 ^ K12 at the GUT scale, there are light exotic coloured fermions in the range 300-400 GeV, together with a light exotic coloured scalar as before.

The inert Higgs masses may be very light depending on the particular parameters chosen. For example, for benchmarks B and E the lightest inert Higgs bosons of the first and second generation have relatively small masses (mH1 i = 154 GeV and mH1i = 220 GeV respectively). For all the benchmarks the inert Higgsinos are light, as ¡if,. = 230-300 GeV.

The lightest stop mass is in the range 430-550 GeV for all the benchmark points, with the remaining squark and slepton masses being all significantly heavier than the stop mass but below 1 TeV. Note that the gluino mass, being below 350 GeV, is always lighter than all the squark masses for all the benchmark points.

6. Conclusions

We have discussed the predictions of a constrained version of the exceptional supersymmetric standard model (cE6SSM), based on a universal high energy soft scalar mass m0, soft trilinear mass A0 and soft gaugino mass Mi/2. We have seen that the cE6SSM predicts a characteristic SUSY spectrum containing a light gluino, a light wino-like neutralino and chargino pair, and a light bino-like neutralino, with other sparticle masses except the lighter stop be-

ing much heavier. In addition, the cE6SSM allows the possibility of light exotic colour triplet charge 1 /3 fermions and scalars, leading to early exotic physics signals at the LHC.

We have focussed on the possibility of low values of (m0, M1/2) < (700,400) GeV, and a Z' gauge boson with mass close to 1 TeV, which would correspond to an early LHC discovery using "first data", and have proposed a set of benchmark points to illustrate this in Table 3 and Fig. 2. For some of the benchmarks (C and D) there are exotic colour triplet charge ±1/3 D fermions and scalars below 500 GeV, with distinctive final states as discussed in Section 5.1.2. All the benchmark points have a SM-like Higgs close to the LEP2 limit of 115 GeV with the rest of the Higgs spectrum significantly heavier. The inert Higgs bosons may be relatively light, but will be difficult to produce, having zero VEVs and small couplings to quarks and leptons. The lightest stop mass is in the range 430-550 GeV for all the benchmark points, with the remaining squark and slepton masses being all significantly heavier than the stop mass but below 1 TeV. The gluino mass is very light, being below 350 GeV in all cases, and in particular is lighter than the stop squark for all the benchmark points. The chargino and second neutralino masses are just above the LEP2 limit of 100 GeV, while the lightest neutralino is around 60 GeV.

We have not considered the question of cosmological cold dark matter (CDM) relic abundance due to the neutralino LSP and so one may be concerned that a bino-like lightest neutralino mass of around 60 GeV might give too large a contribution to i?CDM. Indeed a recent calculation of i?CDM in the USSM [22], which includes the effect of the MSSM states plus the extra Z' and the active singlet S, together with their superpartners, indicates that for the benchmarks considered here that i?CDM would be too large. However the USSM does not include the effect of the extra inert Higgs and Higgsinos that are present in the EgSSM. While we have considered the inert Higgsino masses given by = Xas/V2, we have not considered the mass of the inert singlinos. These are generated by mixing with the Higgs and inert Higgsinos, and are thus of order fv2/s, where f are additional Yukawa couplings that we have not specified in our analysis. Since s ^ v it is quite likely that the LSP neutralino in the cE6SSM will be an inert singlino with a mass lighter than 60 GeV. This would imply that the state X10 considered here is not cosmologically stable but would decay into lighter (essentially inert) singlinos. Such inert singlinos can annihilate via an s-channel Z-boson, due to their doublet component, yielding an acceptable CDM relic abundance, as has been recently been demonstrated in the E6SSM [23]. The question of the calculation of the relic abundance of such an LSP singlino within the framework of the cE6SSM is beyond the scope of this Letter and will be considered elsewhere. In summary, it is clear that one

should not regard the benchmark points with |mX01 ^ 60 GeV as

being excluded by i?CDM.

To conclude, in this Letter we have argued that the cE6SSM is a very well motivated SUSY model and leads to distinctive predictions at the LHC. We have presented sample benchmark points for which not only the Higgs boson, but also SUSY particles such as gauginos and stop, and even more exotic states such as a light Z' and colour triplet charge ±1/3 D fermions and scalars, could be just around the corner in early LHC data. If such states are discovered, this would not only represent a revolution in particle physics, but would also point towards an underlying high energy E6 gauge structure, providing a window into string theory.

Acknowledgements

We would like to thank A. Belyaev, C.D. Froggatt and D. Sutherland for fruitful discussions. R.N. is also grateful to E. Boos,

M.I. Vysotsky and P.M. Zerwas for valuable comments and remarks. D.J.M. acknowledges support from the STFC Advanced Fellowship grant PP/C502722/1. R.N. acknowledges support from the SHEFC grant HR03020 SUPA 36878. S.F.K. acknowledges partial support from the following grants: STFC Rolling Grant ST/G000557/1 (also S.M.); EU Network MRTN-CT-2004-503369; NATO grant PST.CLG.980066 (also S.M.); EU ILIAS RII3-CT-2004-506222. S.M. is also partially supported by the FP7 RTN MRTN-CT-2006-035505.

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